Let's go through an example, using the marginal and chief ray, in a fairly real system. And along the way we'll learn a cover optical design, named for a guy named Lyot. Lyot solved the problem of what if you'd like to look at, let's say a star and right near that star is a planet. So you want to image the planet and reject the light from the star. So clearly stops are going to be important in this kind of problem. And so this Lyot stop, is a concept that's used to block scatter and really intense sources cause some extra problems in optical systems. So it's a thing to know about. It's not nearly as fundamental as the field and aperture stop, it's just a useful example of the concepts. Let's imagine we built ourselves a telescope, we'll have some front optic, could be a mirror or a lens, I've drawn in it here as a lens to make the retracing easy. The object is out here at infinity or darn close to it. And so my rays are coming in essentially parallel. I'm going to form a first image of whatever my telescope is looking at. And then I'm going to reimage that with a second lens and this is the classic telescope design, this might be an eyepiece let's say, and it simply gives you some more magnification after the primary lens here get grabs all the light and forms the first image. So let's go through and do our analysis. The first thing we did do is launch a ray off of the object. We're going to tilt it up until it runs into some stop and we're going to call that the aperture stop. Now since the object is infinitely far away, when I tilt a ray off of the object, all that seems to do here at my optical system is increase the ray heighth or increase or decrease. And that's because I'm far away. So my objects out here at infinity, I increase the angle of the light getting off of the object, which after my optical system seems to be a parallel ray whose heighths just increases and a well designed telescope would always have that first optic be the aperture stop. You want to gather all the light you can and you're going to make that first optic grab all that light. So in this case my objective, my first element in my optical system will be our aperture stop. And so there's my marginal ray going through the system. Now I launch a ray from the center of the aperture stop and I tilt it, it's now going off in the object space at some angle here. It goes into the system and hits any intermediate stop, that in this case, I'm on my previous example has been put at an image plane. That's a good place now to put my field top. So that my field stop is in focus, light that's at larger angle coming into this system which would correspond to larger field points out there at infinity, all gets blocked exactly at once, and then once I'm at angles smaller than my angular field of view, all the light get through the field stop because the field stop is at an image plane or one conjugate to it. All right, so I have my marginal and my chief rays, great. The problem we have solved is this, if I look now here at my image plane and what I'd like to do is look at an object that's a little bit to the side of my really bright source. That bright source let's say, is just outside my angular field of view. So it's coming in a little bit bigger angle and my chief ray and it's getting blocked by the field stop. Yay, that's great. But it also is fully illuminating perhaps many orders of magnitude brighter than the object I want to look at. My objective lens here, my aperture stop and there's going to be a lot of scatter off of the edge of this lens. And this is the simple version of it where the lens is held up in a circular mount. If this was a mirror, there might be some sort of superstructure here, so that there were veins and mechanical structure literally in the field of view itself. And so, at the edge of each of those, I'm going to get this enormous scatter from this really bright source that's, I'm blocking the image at the source itself but it's still going to scare off of my aperture stop. But if I look over here, I noticed that scatter has come back into focus. And I could imagine now putting a stop here specifically to block the scatter from the edge of my aperture stop. Where would I do that? Where would I find all of the light from the aperture stop comes back into focus? Well, that of course is the exit pupil, it's the image of the aperture stop in the image space. So this is an example of knowing where that exit pupil is, and having it in a convenient place is pretty important because now I can take, I can put extra stop right here in my exit pupil and I can make it just a little bit smaller, I can squeeze this new stop down a little bit smaller than the exit pupil, and that's going to block all that scattered light. It'll cause just a slight decrease in performance of my optical system, but I now won't have this big glow coming from the edge of the system. And if I had a more complex aperture here because it was something like a mirror, I can shape the Lyot stop, to put barriers or something sort of a blocking feature over whereever I thought I should, I was going to get scatter there. And again, that would lose me some performance of my image plane, but it would massively increase my signal to noise. So this is an example of where exit pupils can be something you want to design, you want to put them in a particular place because they may be something you want to use to improve the performance of your system.
